# How do you find the inflection points of f(x)=x^5-30x^3?

Aug 31, 2016

0 and -3

#### Explanation:

$\mathrm{df} \left(x\right) = 5 {x}^{4} - 90 {x}^{2}$
$d \left(\mathrm{df} \left(x\right)\right) = 20 {x}^{3} - 180 x$
$20 {x}^{3} - 180 x = 0$
x=0; x=3; x=-3
$g \left(x\right) = d \left(d \left(\mathrm{df} \left(x\right)\right)\right) = 60 {x}^{2} - 180$
g(0)=-180; g(3)=0; g(-3)=1080
3 is not infection point.